{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2025 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# set_covering_deployment"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/contrib/set_covering_deployment.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/contrib/set_covering_deployment.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "  Set covering deployment in Google CP Solver\n",
    "\n",
    "  From http://mathworld.wolfram.com/SetCoveringDeployment.html\n",
    "  '''\n",
    "  Set covering deployment (sometimes written 'set-covering deployment'\n",
    "  and abbreviated SCDP for 'set covering deployment problem') seeks\n",
    "  an optimal stationing of troops in a set of regions so that a\n",
    "  relatively small number of troop units can control a large\n",
    "  geographic region. ReVelle and Rosing (2000) first described\n",
    "  this in a study of Emperor Constantine the Great's mobile field\n",
    "  army placements to secure the Roman Empire.\n",
    "  '''\n",
    "\n",
    "  Compare with the following models:\n",
    "  * MiniZinc: http://www.hakank.org/minizinc/set_covering_deployment.mzn\n",
    "  * Comet   : http://www.hakank.org/comet/set_covering_deployment.co\n",
    "  * Gecode  : http://www.hakank.org/gecode/set_covering_deployment.cpp\n",
    "  * ECLiPSe : http://www.hakank.org/eclipse/set_covering_deployment.ecl\n",
    "  * SICStus : http://hakank.org/sicstus/set_covering_deployment.pl\n",
    "\n",
    "  This model was created by Hakan Kjellerstrand (hakank@gmail.com)\n",
    "  Also see my other Google CP Solver models:\n",
    "  http://www.hakank.org/google_or_tools/\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.constraint_solver import pywrapcp\n",
    "\n",
    "\n",
    "def main():\n",
    "\n",
    "  # Create the solver.\n",
    "  solver = pywrapcp.Solver(\"Set covering deployment\")\n",
    "\n",
    "  #\n",
    "  # data\n",
    "  #\n",
    "\n",
    "  countries = [\n",
    "      \"Alexandria\", \"Asia Minor\", \"Britain\", \"Byzantium\", \"Gaul\", \"Iberia\",\n",
    "      \"Rome\", \"Tunis\"\n",
    "  ]\n",
    "  n = len(countries)\n",
    "\n",
    "  # the incidence matrix (neighbours)\n",
    "  mat = [[0, 1, 0, 1, 0, 0, 1, 1], [1, 0, 0, 1, 0, 0, 0, 0],\n",
    "         [0, 0, 0, 0, 1, 1, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0],\n",
    "         [0, 0, 1, 0, 0, 1, 1, 0], [0, 0, 1, 0, 1, 0, 1, 1],\n",
    "         [1, 0, 0, 1, 1, 1, 0, 1], [1, 0, 0, 0, 0, 1, 1, 0]]\n",
    "\n",
    "  #\n",
    "  # declare variables\n",
    "  #\n",
    "\n",
    "  # First army\n",
    "  X = [solver.IntVar(0, 1, \"X[%i]\" % i) for i in range(n)]\n",
    "\n",
    "  # Second (reserv) army\n",
    "  Y = [solver.IntVar(0, 1, \"Y[%i]\" % i) for i in range(n)]\n",
    "\n",
    "  #\n",
    "  # constraints\n",
    "  #\n",
    "\n",
    "  # total number of armies\n",
    "  num_armies = solver.Sum([X[i] + Y[i] for i in range(n)])\n",
    "\n",
    "  #\n",
    "  #  Constraint 1: There is always an army in a city\n",
    "  #                (+ maybe a backup)\n",
    "  #                Or rather: Is there a backup, there\n",
    "  #                must be an an army\n",
    "  #\n",
    "  [solver.Add(X[i] >= Y[i]) for i in range(n)]\n",
    "\n",
    "  #\n",
    "  # Constraint 2: There should always be an backup army near every city\n",
    "  #\n",
    "  for i in range(n):\n",
    "    neighbors = solver.Sum([Y[j] for j in range(n) if mat[i][j] == 1])\n",
    "    solver.Add(X[i] + neighbors >= 1)\n",
    "\n",
    "  objective = solver.Minimize(num_armies, 1)\n",
    "\n",
    "  #\n",
    "  # solution and search\n",
    "  #\n",
    "  solution = solver.Assignment()\n",
    "  solution.Add(X)\n",
    "  solution.Add(Y)\n",
    "  solution.Add(num_armies)\n",
    "  solution.AddObjective(num_armies)\n",
    "\n",
    "  collector = solver.LastSolutionCollector(solution)\n",
    "  solver.Solve(\n",
    "      solver.Phase(X + Y, solver.INT_VAR_DEFAULT, solver.INT_VALUE_DEFAULT),\n",
    "      [collector, objective])\n",
    "\n",
    "  print(\"num_armies:\", collector.ObjectiveValue(0))\n",
    "  print(\"X:\", [collector.Value(0, X[i]) for i in range(n)])\n",
    "  print(\"Y:\", [collector.Value(0, Y[i]) for i in range(n)])\n",
    "\n",
    "  for i in range(n):\n",
    "    if collector.Value(0, X[i]) == 1:\n",
    "      print(\"army:\", countries[i], end=\" \")\n",
    "    if collector.Value(0, Y[i]) == 1:\n",
    "      print(\"reserv army:\", countries[i], \" \")\n",
    "  print()\n",
    "\n",
    "  print()\n",
    "  print(\"failures:\", solver.Failures())\n",
    "  print(\"branches:\", solver.Branches())\n",
    "  print(\"WallTime:\", solver.WallTime())\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
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